S. Shelah

activity

19922026

most citedThe monadic theory of order

324 citations · 1.7k across the 753 of their papers we have counts for

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755 papers · 1 filter

math.LO2026

Kaplansky decompositions of Polish modules

Ivo Herzog, Gianluca Paolini, Saharon Shelah

Let $R$ be a countable ring. Given an $R$ -module $A$ , we call a decomposition $A = ⨁_{i \in I} N_{i}$ a Kaplansky decomposition if each $N_{i}$ is countable. We characterize th…

math.LO2025

Adding the constant evasion and constant prediction numbers to Cichoń's maximum

Miguel A. Cardona, Miroslav Repický, Saharon Shelah

Let $e_{2}^{const}$ be the constant evasion number, that is, the size of the least family $F \subseteq^{ω} 2$ of reals such that for each predictor $π\colon {}^{<ω}2\…

math.LO2025

Forcing Diamond and Applications to Iterability

Heike Mildenberger, Saharon Shelah

We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence. We answer the longstanding que…

math.LO2025

An analogue of U-rank for atomic classes

John T. Baldwin, Michael C. Laskowski, Saharon Shelah

For a countable, complete, first-order theory $T$ , we study $A t$ , the class of atomic models of $T$ . We develop an analogue of $U$ -rank and prove two results. On one hand, if some…

math.LO2025

On a problem of Erdos and Hajnal

Shimon Garti, Yair Hayut, Saharon Shelah

We address a question of Erdős and Hajnal about the ordinary partition relation $ℵ_{ω + 1} ↛ (ℵ_{ω + 1}, (3)_{ℵ_{0}})^{2}$ . For $θ = cf (λ) < λ$ , assuming $2^λ=λ…

math.LO2025

More separations of cardinal characteristics of the strong measure zero ideal

Miguel A. Cardona, Miroslav Repický, Saharon Shelah

Let $N$ be the $σ$ -ideal of the null sets of reals. We introduce a new property of forcing notions that enable control of the additivity of $N$ after finite sup…