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Preprint Number 2003
2003. JinHoo Ahn, Joonhee Kim, and Junguk Lee On the Antichain Tree Property E-mail: Submission date: 16 June 2021. Revised version: 7 February 2022. Abstract: In this note, we investigate a new model theoretical tree property, called the antichain tree property (ATP). We develop combinatorial techniques for ATP. First, we show that ATP is always witnessed by a formula in a single free variable, and for formulas, not having ATP is closed under disjunction. Second, we show the equivalence of ATP and k-ATP, and provide a criterion for theories to have not ATP (being NATP). Mathematics Subject Classification: 2010: 03C45, 03C60, 12J10, 05C25 Keywords and phrases: |
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