### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

b-scale Whitehead Problem Erdos Cardinal 05A17 Commutative cancellative semigroups Rado's conjecture S-Space Fat stationary set Hindman's Theorem Distributive tree Constructible Universe Parameterized proxy principle Weakly compact cardinal Selective Ultrafilter very good scale Cardinal function Chromatic number Mandelbrot set square principles Forcing weak square Knaster Kurepa Hypothesis Coherent tree Diamond Hereditarily Lindelöf space Nonspecial tree Erdos-Hajnal graphs Jonsson cardinal diamond star 11P99 Singular cardinals combinatorics weak diamond Ostaszewski square Fast club Slim tree Luzin set Almost Souslin Almost countably chromatic stationary hitting Uniformization Partition Relations Almost-disjoint famiy polarized partition relation Club Guessing Chang's conjecture Foundations Square-Brackets Partition Relations Small forcing tensor product graph ccc Souslin Tree square Sakurai's Bell inequality Poset 05D10 approachability ideal Uniformly coherent 20M14 Successor of Singular Cardinal Hedetniemi's conjecture Singular Density Forcing Axioms coloring number Reduced Power Axiom R Antichain reflection principles Ascent Path free Boolean algebra Large Cardinals Microscopic Approach Martin's Axiom HOD Generalized Clubs incompactness Cardinal Invariants P-Ideal Dichotomy Cohen real Aronszajn tree Fodor-type reflection Prevalent singular cardinals stationary reflection projective Boolean algebra PFA(S)[S] Rainbow sets Prikry-type forcing Universal Sequences Singular coﬁnality Successor of Regular Cardinal middle diamond L-space Shelah's Strong Hypothesis sap PFA xbox Dushnik-Miller Minimal Walks Rock n' Roll Absoluteness OCA Stevo Todorcevic Postprocessing function Non-saturation

# Tag Archives: 03E65

## A Microscopic approach to Souslin-tree constructions. Part I

Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading

Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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## Reduced powers of Souslin trees

Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading

## A topological reflection principle equivalent to Shelah’s strong hypothesis

Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading

Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Shelah's Strong Hypothesis
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## Openly generated Boolean algebras and the Fodor-type reflection principle

Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading

## On guessing generalized clubs at the successors of regulars

Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading