| Axiom of choice | D0AR7TD1GP | statement | open | Wikipedia List of first-order theories#HJUZ |
| Axiom of choice | EV733FA6VJ | statement | open | Wikipedia Kőnig's theorem (set theory)#6VIP |
| Axiom of choice | GPADVCY5KW | statement | open | Wikipedia Product topology#CF8Z |
| Axiom of Choice | J2DGJDAB6J | statement | open | ernst_ibl MAAPressVersion/IndexingSets.tex#axiom-1 |
| Axiom of choice | RZ3HV9M29W | statement | open | Wikipedia List of mathematical logic topics#HSVY |
| Axiom of choice | S1KQET8VK6 | statement | open | Wikipedia Set (mathematics)#431S |
| Axiom of choice in type theory | FKDX1K9M8D | statement | open | Wikipedia Axiom of choice#TVQV |
| Axiom of completeness | GJTXEMNCS1 | statement | open | Wikipedia Nested intervals#9GQ6 |
| axiom of constructibility | 1Y14Y1S86N | statement | open | Wikidata Q1151112, nLab axiom of constructibility, Wikipedia Axiom of constructibility |
| Axiom of constructibility | 4WYVT7F6KX | statement | open | Wikipedia List of axioms#HWCZ |
| Axiom of constructibility | 7D5J2VGNHH | statement | open | Wikipedia List of first-order theories#KG9A |
| Axiom of constructibility | H9VNSJYCW1 | statement | open | Wikipedia List of statements independent of ZFC#10IB |
| Axiom of countability | BXWF3JNVDD | statement | open | Wikipedia List of general topology topics#IDM1 |
| Axiom of countability | ERSA1RNWFG | statement | open | Wikipedia Axiom of countability, Wikidata Q336779 |
| Axiom of countability | T6N947ZP29 | statement | open | Wikipedia List of axioms#L1JH |
| Axiom of countable choice | 96WQ6SGC7R | statement | open | Wikipedia List of axioms#G0MV |
| axiom of countable choice | AJM2A819TK | statement | open | Wikidata Q1000116, nLab countable choice, ProofWiki Axiom:Axiom_of_Countable_Choice, Wikipedia Axiom of countable choice |
| axiom of dependent choice | 7TS9362SR2 | statement | open | Wikidata Q3303153, nLab dependent choice, ProofWiki Axiom:Axiom_of_Dependent_Choice, Wikipedia Axiom of dependent choice |
| Axiom of dependent choice | XPQ2981X4X | statement | open | Wikipedia List of axioms#JWDJ |
| axiom of determinacy | JVP5MFKMNG | statement | open | Wikidata Q4830558, nLab axiom of determinacy, Wikipedia Axiom of determinacy |
| Axiom of determinacy | MH9Y4AVJT6 | statement | open | Wikipedia List of axioms#QGBH |
| Axiom of determinacy | ZZ2KWGPCBK | statement | open | Wikipedia Determinacy#PDYV |
| Axiom of empty set | NFDVTE6J64 | statement | open | Wikipedia List of axioms#G53M |
| axiom of empty set | TVFZ9GW0FT | statement | open | Wikidata Q2045366, ProofWiki Axiom:Axiom_of_the_Empty_Set, Wikipedia Axiom of empty set |
| Axiom of Euclid | Z9PFJRMC9R | statement | open | Wikipedia Tarski's axioms#J73M |
| Axiom of extensionality | E32ERZV3RM | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#P367 |
| axiom of extensionality | H6XPSHRMJR | statement | node (a node has the same Wikidata item as the row) | Wikidata Q740424, MathWorld AxiomofExtensionality, nLab axiom of extensionality, ProofWiki Axiom:Axiom_of_Extension, Wikipedia Axiom of extensionality |
| Axiom of extensionality | RYT91QH6SY | statement | open | Wikipedia List of axioms#AZDF |
| Axiom of extensionality - 1 | FTHTZMA51X | statement | open | Wikipedia Zermelo–Fraenkel set theory#QWOI |
| Axiom of finite choice | ZKYYEGFJ0Q | statement | open | Wikipedia Axiom of finite choice, Wikidata Q30715485 |
| Axiom of global choice | KPYTNDRDZQ | statement | open | Wikipedia List of axioms#30QL |
| Axiom of global choice | MWVR4YDS3D | statement | open | Wikipedia Axiom of global choice, Wikidata Q3511558 |
| Axiom of global choice | VGY0Z6Z5ZM | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#4VYW |
| Axiom of global choice | WTP7AYMJGB | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#K1LP |
| Axiom of Induction | A9QGDXSQF5 | statement | open | ernst_ibl MAAPressVersion/IntroInduction.tex#axiom:induction |
| Axiom of infinity | 94TB12C2H9 | statement | open | Wikipedia List of axioms#6JGT |
| axiom of infinity | XNAM6DTABT | statement | open | Wikidata Q920450, MathWorld AxiomofInfinity, nLab axiom of infinity, ProofWiki Axiom:Axiom_of_Infinity, Wikipedia Axiom of infinity |
| Axiom of infinity - 7 | 37RMNW7SE4 | statement | open | Wikipedia Zermelo–Fraenkel set theory#HKAK |
| axiom of limitation of size | A7BKMQ06WX | statement | open | Wikidata Q836475, ProofWiki Axiom:Axiom_of_Limitation_of_Size, Wikipedia Axiom of limitation of size |
| Axiom of non-choice | WC8CHCVVRD | statement | open | Wikipedia Axiom of non-choice, Wikidata Q28456649 |
| axiom of pairing | 207C4VY66G | statement | open | Wikidata Q920796, MathWorld AxiomoftheUnorderedPair, nLab axiom of pairing, ProofWiki Axiom:Axiom_of_Pairing, Wikipedia Axiom of pairing |
| Axiom of pairing | F79ZV2ZRS7 | statement | open | Wikipedia List of axioms#7G5D |
| Axiom of pairing | J3RS50GZQN | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#TVV0 |
| Axiom of pairing - 4 | 6C6Z28YRV5 | statement | open | Wikipedia Zermelo–Fraenkel set theory#U5A8 |
| Axiom of Pasch | WM63FSY9PT | statement | open | Wikipedia Tarski's axioms#KH1K |
| Axiom of power set | 3Y50G20NA6 | statement | open | Wikipedia List of axioms#UBIE |
| Axiom of power set | 9HPTB63YR5 | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#IP8P |
| axiom of power set | FVZH3BH74M | statement | open | Wikidata Q1077811, MathWorld AxiomofthePowerSet, ProofWiki Axiom:Axiom_of_Powers, Wikipedia Axiom of power set |
| Axiom of power set - 8 | EJ15JAWXTH | statement | open | Wikipedia Zermelo–Fraenkel set theory#5989 |
| Axiom of projective determinacy | AMKJRCYYPT | definition | open | Wikipedia List of axioms#B0M3 |
| Axiom of real determinacy | QVQRWJJ2E1 | statement | open | Wikipedia Axiom of real determinacy, Wikidata Q4830559 |
| Axiom of real determinacy | X4NC3EJFY5 | statement | open | Wikipedia List of axioms#PCKR |
| Axiom of reducibility | N4RAWC22K4 | statement | open | Wikipedia Axiom of reducibility, Wikidata Q4830560 |
| axiom of regularity | KDRCAA787D | statement | open | Wikidata Q470981, MathWorld AxiomofFoundation, nLab axiom of foundation, ProofWiki Axiom:Axiom_of_Foundation, Wikipedia Axiom of regularity |
| Axiom of regularity | WDV1HNMYWA | statement | open | Wikipedia List of axioms#BV0A |
| Axiom of regularity (also called the axiom of foundation) - 2 | T3NFX12BX8 | statement | open | Wikipedia Zermelo–Fraenkel set theory#DQUM |
| Axiom of uniformization | 42ZNDXX2HB | definition | open | Wikipedia List of axioms#MIPW |
| Axiom of union | 2D21HE6E9D | statement | open | Wikipedia List of axioms#A2Y5 |
| axiom of union | 8EFMNRXQ4K | statement | open | Wikidata Q1987722, MathWorld AxiomoftheSumSet, nLab axiom of union, ProofWiki Axiom:Axiom_of_Unions, Wikipedia Axiom of union |
| Axiom of union | FG9GQ725FK | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#3WKJ |
| Axiom of union - 5 | J9YHVAKAYN | statement | open | Wikipedia Zermelo–Fraenkel set theory#AA2M |
| Axiom of well-ordering (choice) - 9 | F24J3NCDBG | statement | open | Wikipedia Zermelo–Fraenkel set theory#P7Q2 |
| Axiom schema | 9JZA8FKNR7 | statement | open | Wikipedia Axiom schema, Wikidata Q792536 |
| Axiom schema of continuity | 9W8ZG9VK9X | statement | open | Wikipedia Tarski's axioms#99JI |
| Axiom schema of predicative separation | J9MAQ0MQXN | statement | open | Wikipedia Axiom schema of predicative separation, Wikidata Q4830561 |
| axiom schema of replacement | R9Y22E1MPJ | statement | open | Wikidata Q1361825, MathWorld AxiomofReplacement, nLab axiom of replacement, ProofWiki Axiom:Axiom_of_Replacement, Wikipedia Axiom schema of replacement |
| Axiom schema of replacement | S712WSCE6Y | statement | open | Wikipedia List of axioms#MBS2 |
| Axiom schema of replacement - 6 | 298AY5X0X1 | statement | open | Wikipedia Zermelo–Fraenkel set theory#S438 |
| axiom schema of specification | W6NJS0ZRFW | statement | open | Wikidata Q780487, MathWorld AxiomsofSubsets, ProofWiki Axiom:Axiom_of_Specification, Wikipedia Axiom schema of specification |
| Axiom schema of specification | ZF3GZMF522 | statement | open | Wikipedia List of axioms#18SZ |
| Axiom schema of specification (or of separation, or of restricted comprehension) - 3 | KQV73ZB2PT | statement | open | Wikipedia Zermelo–Fraenkel set theory#9WXK |
| Axiom schema of unrestricted comprehension | PKX94593FW | unknown | open | Wikipedia Axiom schema of specification#1M7G |
| Axiom schema versus class existence theorem | 83D3SQ1RVN | statement | open | Wikipedia Von Neumann–Bernays–Gödel set theory#FPE8 |
| Axiom system | K6E7486Q0X | statement | open | Wikipedia Implicational propositional calculus#Y6KI |
| Axiom systems | 5D8QBGANYP | statement | open | Wikipedia Conditional logic#LWH8 |
| Axiom systems | 71CHYRTW9G | statement | open | Wikipedia Epistemic modal logic#00W0 |
| Axiom systems | S6W55BH7EE | statement | open | Wikipedia Mereology#KDNS |
| axiom, of $\Delta_0$-separation | QTTCGQNV96 | concept | open | hott_book index/C.5/axiom-of-delta-0-separation |
| axiom, of choice | 1A79FFP1NQ | concept | open | hott_book index/2/axiom-of-choice |
| axiom, of choice | 1V7XESQ563 | concept | open | hott_book index/u1.u7/axiom-of-choice |
| axiom, of choice | 3JES2X1VT0 | concept | open | hott_book index/9.11/axiom-of-choice |
| axiom, of choice | 4JXBTXSH50 | concept | open | hott_book index/9.8/axiom-of-choice |
| axiom, of choice | 91B5M0RMF6 | concept | open | hott_book index/C.2/axiom-of-choice |
| axiom, of choice | E0B4PMXY56 | concept | open | hott_book index/2.9/axiom-of-choice |
| axiom, of choice | Q5RRCB3NSJ | concept | open | hott_book index/C.1.5/axiom-of-choice |
| axiom, of choice | QE7M9PTK2D | concept | open | hott_book index/C.4/axiom-of-choice |
| axiom, of choice, countable | E9VC2RDB1N | concept | open | hott_book index/B.6/axiom-of-choice-countable |
| axiom, of choice, countable | H6SSRMN9AY | concept | open | hott_book index/B/axiom-of-choice-countable |
| axiom, of choice, countable | SG3VRPWE54 | concept | open | hott_book index/B.4/axiom-of-choice-countable |
| axiom, of choice, type-theoretic | 861NGQJ565 | concept | open | hott_book index/A.6/axiom-of-choice-type-theoretic |
| axiom, of choice, type-theoretic | R6M30QV96T | concept | open | hott_book index/1.15/axiom-of-choice-type-theoretic |
| axiom, of choice, type-theoretic | WWHWK5DSM4 | concept | open | hott_book index/9.2/axiom-of-choice-type-theoretic |
| axiom, of extensionality | 6XA9AFKG4R | concept | open | hott_book index/C.3/axiom-of-extensionality |
| axiom, of infinity | BR56ACA2EG | concept | open | hott_book index/C.5/axiom-of-infinity |
| axiom, of reducibility | BD5NZ3HNH1 | concept | open | hott_book index/9.11/axiom-of-reducibility |
| axiom, of replacement | VJZ25V8B78 | concept | open | hott_book index/C.5/axiom-of-replacement |
| axiom, of separation | C667CC87WV | concept | open | hott_book index/C.5/axiom-of-separation |
| axiom, of set theory, for the cumulative hierarchy | HNE0170GHG | concept | open | hott_book index/C.5/axiom-of-set-theory-for-the-cumulative-hierarchy |
| axiom, Streicher's Axiom K | KQEY0BX2V9 | concept | open | hott_book index/6.7/axiom-streicher-s-axiom-k |
| axiom, Streicher's Axiom K | Q6QGZ3SQW7 | concept | open | hott_book index/A.12.3/axiom-streicher-s-axiom-k |
