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HOD Well-behaved magma Large Cardinals Intersection model Slim tree GMA Reduced Power Luzin set Lipschitz reduction higher Baire space Souslin Tree Generalized Clubs tensor product graph 54G20 reflection principles P-Ideal Dichotomy Hedetniemi's conjecture Sakurai's Bell inequality Amenable C-sequence positive partition relation ZFC construction Successor of Singular Cardinal Postprocessing function coloring number Iterated forcing Fodor-type reflection Rainbow sets weak Kurepa tree Club Guessing Singular cofinality Weakly compact cardinal Precaliber PFA Coherent tree diamond star Forcing O-space Diamond-sharp Closed coloring square Microscopic Approach countably metacompact b-scale Shelah's Strong Hypothesis Small forcing Analytic sets regressive Souslin tree Absoluteness Martin's Axiom stationary reflection SNR Axiom R Dushnik-Miller Mandelbrot set Whitehead Problem Ulam matrix Uniformly homogeneous Hindman's Theorem Chromatic number middle diamond Filter reflection projective Boolean algebra free Souslin tree Uniformly coherent club_AD Chang's conjecture Diamond for trees Strongly compact cardinal free Boolean algebra Fast club Countryman line Cardinal function Respecting tree ccc Rado's conjecture Local Club Condensation. strongly bounded groups Foundations Hereditarily Lindelöf space Ineffable cardinal Partition Relations Antichain Ostaszewski square Strong coloring polarized partition relation approachability ideal Erdos-Hajnal graphs xbox C-sequence Selective Ultrafilter Strongly Luzin set Cardinal Invariants L-space Forcing Axioms sap Minimal Walks full tree incompactness very good scale Subadditive Subtle cardinal Ramsey theory over partitions Rock n' Roll Successor of Regular Cardinal Ascent Path indecomposable ultrafilter Erdos Cardinal Greatly Mahlo Commutative projection system Uniformization Fat stationary set Vanishing levels Parameterized proxy principle Commutative cancellative semigroups stationary hitting Distributive tree Reflecting stationary set OCA stick AIM forcing Sigma-Prikry Sierpinski's onto mapping principle Generalized descriptive set theory Cohen real Was Ulam right? Square-Brackets Partition Relations Knaster and friends PFA(S)[S] Almost-disjoint family transformations Universal Sequences square principles Aronszajn tree Almost countably chromatic Poset Prikry-type forcing S-Space unbounded function Constructible Universe Non-saturation weak square Diamond super-Souslin tree Almost Souslin specializable Souslin tree Open Access Jonsson cardinal Nonspecial tree Prevalent singular cardinals Dowker space Kurepa Hypothesis Singular cardinals combinatorics Knaster Subnormal ideal weak diamond Singular Density nonmeager set Subtle tree property
Tag Archives: ZFC construction
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Prikry-type forcing, ZFC construction
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A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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Partitioning a reflecting stationary set
Joint work with Maxwell Levine. Abstract. We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer … Continue reading
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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Mathematics Colloquium, Bar-Ilan University, November 2013
I gave a colloquium talk at Bar-Ilan University on November 10, 2013. Title: Forcing as a tool to prove theorems Abstract: Paul Cohen celebrated solution to Hilbert’s first problem showed that the Continuum Hypothesis is independent of the usual axioms of … Continue reading
Rectangular square-bracket operation for successor of regular cardinals
Joint work with Stevo Todorcevic. Extended Abstract: Consider the coloring statement
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal
