Revision #204 → #1388 · back to history
addedMathematical logic2120f82bcc21
addedFormalization of mathematics in set theory508f6772cab9
addedArithmetic as theory of natural numbers82b77910b240
addedPeano axiomsc7b273ce5e30
addedInduction characterization of the naturals (Dedekind)98c2dfb3e358
addedUniqueness of the naturals up to isomorphismed266b326472
addedIndependence of the parallel postulatea14189ac885d
addedTheorem that a line contains at least two pointsb971e72a88cb
addedHilbert's axioms for geometry8919eb08a6a8
addedNowhere-differentiable continuous functions7c8f46279d24
added(ε, δ)-definition of limit (Bolzano)dbd5ca63e0dc
addedCauchy's definition of continuity0f224ab52161
addedDedekind cuts definition of the reals08b59cbbed52
addedReals and naturals have different cardinalities0df37a9354d9
addedUncountability of the reals (diagonal argument)425c35e4b09d
addedCantor's theorem27fac675acd3
addedWell-ordering theorem (Zermelo)5590446a1df6
addedBurali-Forti paradoxa5dad2b22037
addedRussell's paradox46d95ffc6f9a
addedIndependence of choice with urelements (Fraenkel)6fbcb3aa9f31
addedIndependence of the axiom of choice in ZF (Cohen)930bff06b856
addedLöwenheim–Skolem theoremb5983d13a8c2
addedSkolem's paradoxe009bfa00c24
addedGödel's completeness theoremcc165b80ce70
addedCompactness theoremb687550ab440
addedGödel's incompleteness theoremb670961dff9b
addedUnprovability of consistency in-system1e3699aba3da
addedGentzen's consistency proof of arithmeticc4d76942d19e
addedGödel's Dialectica consistency proof71ef149d8fb6
addedFirst-order logic102ee07f754e
addedLöwenheim–Skolem theorem (precise)847131d41268
addedGödel's completeness theorem (precise)6989a28ef28e
addedCompactness theorem (precise)9075c5709ba9
addedFirst incompleteness theorem3b27f65b69ce
addedGödel sentence for Peano axiomscab99d0ff9af
addedEffectively given logical system85bb91102011
addedNon-elementarily-equivalent models from incompleteness11ce75d73675
addedSecond incompleteness theorem3ee2fbfb008a
addedInfinitary logicsddece9effd8d
addedThe infinitary logic L_ω1ω21c2709d0018
addedHigher-order logics1105ed17cbc0
addedHigher-order logic lacks completeness/compactnessa776c93eee06
addedFixed-point logicsafb19e6a4d93
addedExtension of first-order logic08269e987c40
addedLindström's theorem5a606e7cb2f3
addedModal logics51c2944d8635
addedIntuitionistic logic and excluded middlebd780b12f7d1
addedProvably total intuitionistic functions are computable4bcf2518682e
addedAlgebraic logic48e8754a0461
addedBoolean algebras for propositional truth values2dde8d91d807
addedSet theory6cc0cb732ef7
addedZermelo–Fraenkel set theory (ZF)031051579f86
addedAlternative set theories (NBG, MK, NF)6f61c61adce7
addedAxiom of choice553df70beaa5
addedBanach–Tarski paradox1c83a99aa360
addedConsistency of CH with ZF (Gödel)0ecb08e29040
addedIndependence of CH (Cohen)3210b362c6ac
addedLarge cardinals4a765d97886b
addedInaccessible cardinal implies Con(ZFC)3e19129450cc
addedDeterminacy3fb19816b4ca
addedModel theory006fd0fcc501
addedTheory and modelda177f73d54a
addedElementary classb125c26fc736
addedQuantifier elimination for real-closed fields (Tarski)95c5f4c62199
addedMorley's categoricity theorem986619810fd7
addedCountable-model consequence of CH726b31ff3544
addedVaught's conjecture4756f8ded904
addedRecursion theorya411d1ce755a
addedRobustness of the computable functionse76eebf50917
addedGeneralized recursion theory63f2af9ed587
addedAlgorithmically unsolvable problemb67edeb57e27
addedUndecidability of the Entscheidungsproblem0e6f99b77cec
addedUnsolvability of the halting problem770ffe1fcd20
addedUnsolvability of the word problem for groupsdf2b98b8134b
addedBusy beaver problem890972e30fa2
addedHilbert's tenth problemfe84d3c264f7
addedUnsolvability of Hilbert's tenth problem (Matiyasevich)736e30646ef4
addedProof theoryebf757360f78
addedPredicative development of real analysis (Weyl)b692f58e768f
addedGödel–Gentzen negative translation113329627e84
addedCurry–Howard correspondence205f77ac08e1
addedFagin's theorem4049814cdf65
addedConsistency of non-Euclidean geometry via spherical model5b3e5449955a