William Chan

activity

20172019

most citedOrdinal Definability and Combinatorics of Equivalence Relations

2 citations · 7 across the 6 of their papers we have counts for

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9 papers · 1 filter

math.LO2019

Bounds on Continuous Scott Rank

William Chan, Ruiyuan Chen

An analog of Nadel's effective bound for the continuous Scott rank of metric structures, developed by Ben Yaacov, Doucha, Nies, and Tsankov, will be established: Let $L$ …

math.LO2019★ 1 cited

Bounds on Scott Ranks of Some Polish Metric Spaces

William Chan

If $N$ is a proper Polish metric space and $M$ is any countable dense submetric space of $N$ , then the Scott rank of $N$ in the natural firs…

math.LO2019

An Introduction to Combinatorics of Determinacy

William Chan

This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.

math.LO2019

The Destruction of the Axiom of Determinacy by Forcings on $R$ when $Θ$ is Regular

William Chan, Stephen Jackson

$ZF + AD$ proves that for all nontrivial forcings $P$ on a wellorderable set of cardinality less than $Θ$ , $1_{P} ⊩_{P} \neg AD$ . $…

math.LO2019★ 2 cited

Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations

William Chan, Stephen Jackson

Assume $ZF + A D^{+} + V = L (P (R))$ . Let $\approx$ denote the relation of being in bijection. Let $κ \in ON$ and $⟨ E_{α} : α < κ ⟩$ be a se…

math.LO2018

$L (R)$ with Determinacy Satisfies the Suslin Hypothesis

William Chan, Stephen Jackson

The Suslin hypothesis states that there are no nonseparable complete dense linear orderings without endpoints which have the countable chain condition. $\mathsf{ZF + AD^+ + V = L(\…

Bounds on Continuous Scott Rank

Bounds on Scott Ranks of Some Polish Metric Spaces

An Introduction to Combinatorics of Determinacy

The Destruction of the Axiom of Determinacy by Forcings on R when Θ is Regular

Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations

L(R) with Determinacy Satisfies the Suslin Hypothesis

The Destruction of the Axiom of Determinacy by Forcings on $R$ when $Θ$ is Regular

$L (R)$ with Determinacy Satisfies the Suslin Hypothesis