# Search results

*logical perfection*extracted from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver of ideas in model theory, both mathematically (stability theory may be regarded as a way of approximating categoricity) and philosophically...

Selecta Mathematica > 2019 > 25 > 5 > 1-51

Journal of Automated Reasoning > 2019 > 63 > 2 > 415-438

Axiomathes > 2019 > 29 > 3 > 285-288

Algebra and Logic > 2018 > 56 > 6 > 429-442

Annals of Pure and Applied Logic > 2017 > 168 > 9 > 1609-1642

Annals of Pure and Applied Logic > 2017 > 168 > 7 > 1383-1395

Archive for Mathematical Logic > 2017 > 56 > 5-6 > 671-690

**Theorem 0.1**

*Let*$$\mathbf {K}$$ K

*be an abstract elementary class (AEC) with amalgamation and no maximal models. Let*$$\lambda > {LS}(\mathbf {K})$$ λ > LS ( K ) .

*If*$$\mathbf {K}$$ K

*is categorical in*$$\lambda $$ λ ,

*then the model of cardinality*$$\lambda $$ λ

*is Galois-saturated*.This answers a question asked independently by Baldwin and Shelah...

Archive for Mathematical Logic > 2017 > 56 > 3-4 > 423-452

Annals of Pure and Applied Logic > 2017 > 168 > 3 > 651-692

Selecta Mathematica > 2017 > 23 > 2 > 1469-1506

**Theorem 0.1**Let $$\psi $$ ψ be a...

Annals of Pure and Applied Logic > 2016 > 167 > 11 > 1029-1092

Annals of Pure and Applied Logic > 2016 > 167 > 2 > 155-188

Studies in History and Philosophy of Science > 2015 > 53 > Complete > 12-22

Annals of Pure and Applied Logic > 2015 > 166 > 9 > 851-880

Mathematical Logic Quarterly > 59 > 4-5 > 303 - 331

*T*is ℵ

_{1}‐categorical if and only if it is κ‐categorical for all uncountable κ. In this paper we are taking the first steps towards extending Morley's categoricity theorem “to the finite”. In more detail, we are presenting conditions, implying that certain finite subsets of certain ℵ

_{1}‐categorical

*T*have at most one

*n*‐element model for each natural number $n$...

Annals of Pure and Applied Logic > 2013 > 164 > 3 > 230-250