### 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

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

# 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