### 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

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

# 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