Revision #217 → #1410 · back to history
addedFirst-order formulad00e24039608
addedSentence9c7a686e5556
addedExample formulasfc5b734b1ac5
addedFormula defining prime numbers8380c9c589ce
addedFormula defining irreducibility42a264d093fa
addedSatisfiable theoryc2346c0ea5c5
addedComplete theoryef69551899b1
addedTheory of a structure36270b7f00a4
addedGödel's completeness theorem (model iff consistent)fc1e7b9df93f
addedSignature / language80b597277000
addedStructure148c8d925261
addedSignature for ordered ringscec3affc1057
addedModelling a set of sentences833b8bb7f139
addedSubstructure25e3abbafe7f
addedElementary substructureabaef8e69de3
addedElementary substructure preserves modelling12c55b361872
addedAlgebraic numbers vs rationals as substructures4c4e14f6927d
addedEmbedding and elementary embeddingd38c24e0010f
addedEmbedding is injective homomorphismf2eca328ac98
addedReduct and expansion9ab197a6be58
addedCompactness theoremf9e7b7a7eefc
addedCompactness corollary (finite unsatisfiable subset)af865bea2226
addedLöwenheim–Skolem theorem17d88f8d4c48
addedLS: countable and arbitrarily large modelse58cb7e5b387
addedLindström's theoremc51aca7d07a1
addedFormula defining the primes80135d38c4bd
addedFormula defining the evensd4f8bc46401e
addedFormula defining a curve in a fieldf4a9a7f69f59
addedParameter-free vs parametric definabilitydfb20acec36a
addedCurve defined with a parameterca02ce9b80e3
addedQuantifier eliminationfd1d0f0dea9f
addedQE implies quantifier-free definability27d251e14ac5
addedACF has quantifier elimination9b164f1b266d
addedACF formulas are Boolean combinations of polynomial equationsbfd55ad68225
addedModel-complete theory9abc4610f897
addedTarski–Vaught test1ca17cb3264b
addedModel-completeness criterion (existential formulas)d110069a5a3a
addedModel completion and model companion310f241aa74e
addedFinite subsets are definable with parametersbd63e67903de
addedCofinite subsets are definable317c08655458
addedMinimal structure86a6bb31dce2
addedStrongly minimal theory8609f27f0004
addedACF is strongly minimal04d17ec0f554
addedReal numbers are not minimal8419cc4c38a7
addedo-minimal structure64c3f602f0eb
addedDefinable functions and constants39674d962c37
addedInterpretable structures2d169f85e012
addedUndecidability transfers through interpretationeb0d1c07d5f9
addedComplete type realised by a tuplefbaaab550e2d
addedAutomorphism yields same typea9bfa02ef082
addedTypes over the real order line73afc5239c59
addedPartial n-type5a22ff59df2d
addedComplete typec816c6898001
addedIsolated type0db1cd4ff23b
addedType over integers unrealised in the reals3fc9646d6691
addedType-definable setcacf7d94f1ae
addedACF types correspond to prime idealse4d3785cfd68
addedStructures realise their isolated types66e040ebe957
addedAtomic structure785e02bbe480
addedSaturated structure653ddf575ce3
addedHomogeneous structure94686526998d
addedReal line atomic, rationals saturateda018d290e790
addedDefinable subsets form a Boolean algebrab35600f28f90
addedStone space of n-typesd0ff73d8b161
addedStone space is compact; isolated typeseb7d74811286
addedConstructible topology on ACF type space18485728e54e
addedOmitting types theorem7fa618c42fc2
addedExistence of an atomic model84d4284daba9
addedRealising types in an elementary extension639f7780af21
addedSaturated model existence independent of ZFC269a348830f1
addedUltraproduct68764f381176
addedUltrapowerf96e1f6c9ea0
addedŁoś's theorem83c47865821b
addedUltraproduct of models is a model20229d7efcb2
addedKeisler–Shelah theoreme931128ac7ca
addedCategorical theory (original notion)57b487425bf0
addedOnly finite structures are categorical51caae9c63e2
addedκ-categorical theory98973b700ae1
addedRyll-Nardzewski theorem (ω-categoricity)9d877343cac2
addedDense linear orders order-isomorphic to the rationalsbcc95c97eac8
addedFields are not ω-categorical0e434df58b28
addedω-categorical iff oligomorphic automorphism group616ebf3b5f01
addedFraïssé limitsf2f92e2f6a7b
addedMorley's categoricity theoremb6fb265a0073
addedStrongly minimal theories are uncountably categorical382cbff9f32a
addedTotally categorical theorye0edcd7d35ce
addedλ-stable theory9a3335a655fc
addedStable theory7f0601eb0316
addedStability spectrum theorem9cdf25262dc5
addedUnstable, strictly stable, superstableb0a4c02788c9
addedMain gap theorem45371ea9c708
addedMorley rankea1ee83ecc08
addedTotally transcendental theorybb755590e8a3
addedTotally transcendental iff ω-stable (countable)4987a6f3f147
addedSimple and NIP theories3158f7d92f74
addedStable iff NIP and simple8497fe05578c
addedHomogeneous model theory327b2fd6668b
addedQuasiminimally excellent classes880f0935bbf9
addedAbstract elementary classesbd46e3f71723
addedTarski's quantifier elimination results17a9f7d0d3fb
addedTheory of finite fields is decidable (Ax)787179d39070
addedAx–Kochen theorem2365511ff733
addedHrushovski's geometric Mordell–Lang2396b174f539
addedPila's André–Oort theorem385c4de8426f
addedNIP theories and PAC-learnabilitye1067de3a730
addedStable theories and online learnability154c1de4a4fa
addedClassical results fail for finite structures2aa21e93c345
addedSkolem's paradoxcb49b413c81c
addedCompactness equivalent to Boolean prime ideal theorem3d4a4a0da823
addedCH implies saturated ultrapowerc2537d9ceae3
addedGCH implies saturated elementary extensionda615242d3e3