Revision #155 → #1267 · back to history
addedFirst incompleteness theorem (lead statement)36808f543b67
addedSecond incompleteness theorem (lead statement)869bfc43eebd
addedFormal system41c65e6eef7b
addedFirst-order Peano arithmetic as a formal systemc789965e7aef
addedCannot have all three properties558aeade7a3c
addedEffectively axiomatized systemc2283fe9798d
addedEffectively generated theoriesf2f7db33d354
addedTrue arithmeticb1aa6f30f10f
addedSyntactic completenessb657788b7bcc
addedGödel's completeness theorem799683bb4286
addedEuclidean geometry without parallel postulate is incomplete50e2f8aab303
addedDense linear orders incomplete7c01221e1097
addedContinuum hypothesis unprovable in ZFC5abd00ec5623
addedPeano arithmetic is not completedac82f408c2d
addedNo consistent extension of PA is completef616a9d7bb2d
addedConsistency7095907b12ec
addedPA consistent from ZFC but not itselfdb736ebc2732
addedConsistent iff has a modeladf9d02de3a7
addedAll statements as axioms is inconsistentd30b7b51d2e0
addedUnrestricted comprehension inconsistency6cc1be79c7ef
addedRobinson arithmetic suffices66d888579ff5
addedAlgebraically closed fields complete9e13d12999d6
addedEuclidean geometry complete, consistent, effective1fd9857d9335
addedPresburger arithmetic2c8c4b35295f
addedWillard's self-verifying systems427ad0bd16fa
addedPrinciple of explosion39d714201e04
addedNo complete consistent finite axiom list551480f69b64
addedFirst Incompleteness Theorem (Rosser form)10f2780eceee
addedGödel sentence00a29989de9c
addedExtending F by its Gödel sentence stays incompletecc74959808ea
addedGödel sentence has simple syntactic formfd570e95a316
addedMRDP rewriting of the Gödel sentencea2abcc57e3dd
addedGödel sentence is true083888d600a1
addedGödel sentence false in nonstandard modelsaaff1c1fdc64
addedThe liar paradoxeb0f18ac3397
addedTarski's undefinability theoremca27b92e2fde
addedω-consistencya7bcf588b587
addedω-consistency implies consistency745cdcd9e3d5
addedRosser's strengthening72b704cb0c20
addedConsistency formula Cons(F)1b7d5511ee30
addedSecond incompleteness theorem0cbfef510a9a
addedPA proves largest consistent subset consistent396307c8faa9
addedHilbert–Bernays provability conditions358415b33809
addedPA verifies the Hilbert–Bernays conditions7e95a7485ea5
addedF1 cannot prove consistency of F2 proving F1f7c276df2680
addedPRA cannot prove consistency of PAa5457e97792a
addedGentzen's consistency proof3088070ecbd1
addedUndecidable (proof-theoretic sense)088e742cde80
addedCH and AC undecidable81246c01d996
addedWhitehead problem undecidable (Shelah)8266c32ac111
addedChaitin's incompleteness theorem8aefc67cb073
addedParis–Harrington principleb392ecf05228
addedGoodstein's theorem4f132c68c285
addedKruskal's tree theorem52a2d015a671
addedHalting problem undecidable242c13dd506d
addedMatiyasevich's theorem81d6ddc1c8b4
addedEffectively generate an unprovable polynomial63c4f32a3de9
addedRecursively inseparable sets proofaa914a07dd1b
addedGödel number86c4afc566c1
addedASCII encoding exampleaefdb331de7e
addedStatement form (class-sign)6a01eef90da6
addedProvability formula Bew(y)2fd61acd25b5
addedProvable p implies Bew(G(p)) provablee9e021733dc6
addedDiagonal lemmaaf9d009738b1
addedp is undecidable7000b1a63d24
addedBoolos's Berry-paradox constructione9e718f43b42