ﻻ يوجد ملخص باللغة العربية
We prove that there exists a countable $beta$-model in which, for all reals $X$ and $Y$, $X$ is definable from $Y$ if and only $X$ is hyperarithmetical in $Y$. We also obtain some related results and pose some related questions.
Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras $bf A$. We provide a complete classification for the case that $bf A$ is symmetri
We will prove that there exists a model of ZFC+``c= omega_2 in which every M subseteq R of cardinality less than continuum c is meager, and such that for every X subseteq R of cardinality c there exists a continuous function f:R-> R with f[X]=[0,1].
We construct a model of $mathsf{ZF} + mathsf{DC}$ containing a Luzin set, a Sierpi{n}ski set, as well as a Burstin basis but in which there is no a well ordering of the continuum.
We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called emph{Mammen spaces}, where a Mammen space is a triple $(U,mathcal S,math
We work with symmetric extensions based on L{e}vy Collapse and extend a few results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her P.h.d. thesis. We also observe that if $V$ is a model of ZFC, then $DC_{<kappa}$ can be preserved