### 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

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

# 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