We study several combinatorial properties of (mostly definable) ideals on countable sets. In
several cases, we identify critical ideals for such properties in the Katětov order. In particular …

We prove that, in the choiceless Solovay model, every set of reals is H-Ramsey for every
happy family H that also belongs to the Solovay model. This gives a new proof of Törnquist's …

Given a topological Ramsey space (R,≤, r), we extend the notion of semiselective coideal to
sets H⊆ R and study conditions for H that will enable us to make the structure (R, H,≤, r) a …

In this work, I investigate several combinatorial properties of Borel (or co-analytic) ideals on
countable sets. I extend a theorem presented in M. Hru\v {s}\'{a} k, D. Meza-Alc\'antara, E …

Topological Ramsey theory studies a class of combinatorial topological spaces, called
topological Ramsey spaces, unifying the essential features of those combinatorial frames …

We introduce the notion of a weak A2 space (or wA2-space), which generalises spaces
satisfying Todor\v {c} evi\'c's axioms A1-A4 and countable vector spaces. We show that in …

We introduce a notion of strategically selective coideal, and show that tall strategically
selective coideals do not exist under ADR, generalizing a classical theorem of Mathias. We …

The Ramsey theory of the space of equivalence relations with infinite quotients defined on
the set $\mathbb {N} $ of natural numbers is an interesting field of research. We view this …

We study families of infinite block sequences of elements of the space $\FIN_k $. In
particular we study Ramsey properties of such families and Ramsey properties localized to a …

Sets and Computations : REAL GAMES AND STRATEGICALLY SELECTIVE COIDEALS Page 1
REAL GAMES AND STRATEGICALLY SELECTIVE COIDEALS Paul B. Larson Department of …