Complete Lω1,ω‐sentences with maximal models in multiple cardinalities

DOI10.1002/malq.201800010OpenAlexW2995930225MaRDI QIDQ5108873

Ioannis Souldatos, John T. Baldwin

Publication date: 6 May 2020

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06620

Mathematics Subject Classification ID

Properties of classes of models (03C52) Other infinitary logic (03C75) Model theory of denumerable and separable structures (03C15) Categoricity and completeness of theories (03C35) Other model constructions (03C30)

Related Items (4)

Hanf numbers for extendibility and related phenomena ⋮ A lower bound for the Hanf number for joint embedding ⋮ Maximal models up to the first measurable in ZFC ⋮ Kurepa trees and spectra of \(\mathcal{L}_{\omega_1, \omega}\)-sentences

Cites Work

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• The joint embedding property and maximal models
• Linear orderings and powers of characterizable cardinals
• Hanf numbers for extendibility and related phenomena
• Notes on cardinals that are characterizable by a complete (Scott) sentence
• Three red herrings around Vaught’s conjecture
• The Hanf number for complete L_ω1,ω-sentences (without GCH)
• On the existence of atomic models
• KNIGHT'S MODEL, ITS AUTOMORPHISM GROUP, AND CHARACTERIZING THE UNCOUNTABLE CARDINALS
• AMALGAMATION, ABSOLUTENESS, AND CATEGORICITY
• Hanf Numbers and Presentation Theorems in AECs
• Characterizing the powerset by a complete (Scott) sentence
• DISJOINT AMALGAMATION IN LOCALLY FINITE AEC

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