Year:

  1.  6
    Strong Colorings Over Partitions.William Chen-Mertens, Menachem Kojman & Juris Steprāns - 2021 - Bulletin of Symbolic Logic 27 (1):67-90.
    A strong coloring on a cardinal $\kappa $ is a function $f:[\kappa ]^2\to \kappa $ such that for every $A\subseteq \kappa $ of full size $\kappa $, every color $\unicode{x3b3} <\kappa $ is attained by $f\restriction [A]^2$. The symbol $$ \begin{align*} \kappa\nrightarrow[\kappa]^2_{\kappa} \end{align*} $$ asserts the existence of a strong coloring on $\kappa $.We introduce the symbol $$ \begin{align*} \kappa\nrightarrow_p[\kappa]^2_{\kappa} \end{align*} $$ which asserts the existence of a coloring $f:[\kappa ]^2\to \kappa $ which is strong over a partition $p:[\kappa ]^2\to (...)
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  2.  1
    Decidability of Admissibility: On a Problem by Friedman and its Solution by Rybakov.Jeroen P. Goudsmit - 2021 - Bulletin of Symbolic Logic 27 (1):1-38.
    Rybakov proved that the admissible rules of $\mathsf {IPC}$ are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility.
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  3.  2
    Reduction Techniques for Proving Decidability in Logics and Their Meet–Combination.João Rasga, Cristina Sernadas & Walter Carnielli - 2021 - Bulletin of Symbolic Logic 27 (1):39-66.
    Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...)
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  4.  1
    William Chan, An Introduction to Combinatorics of Determinacy, Trends in Set Theory (S. Coskey and G. Sargsyan, Editors), Contemporary Mathematics, Vol. 752, Providence, RI, American Mathematical Society, 2020, Pp. 21–75. [REVIEW]Thilo Weinert - 2021 - Bulletin of Symbolic Logic 27 (1):91-93.
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