arXiv subjects

Desmond Lau

Publications and source records attributed to Desmond Lau.

3 recordsLinked to original sources

arXiv2025

Relative Constructibility via Generalised Sequential Algorithms

We modify Gurevich's definition of sequential algorithms, so that it becomes amenable to computation with arbitrarily large sets on a sufficiently intuitive level. As a result, two classes of abstract algorithms are obtained, namely generalised sequential algorithms (GSeqAs) and generalised sequential algorithms with parameters (GSeqAPs). We derive from each class a relative computability relation on sets which is analogous to the Turing reducibility relation on reals. We then prove that the relative computability relation derived from GSeqAPs is equivalent to the relative constructibility relation in set theory.

cs.LO↗

arXiv2024

Forcing as a Local Method of Accessing Small Extensions

Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees over $V$. Finally, we give a nice characterisation of the complexity of forcing within this framework.

math.LO↗

arXiv2024

Forcing with Language Fragments, Extending Namba Forcing, and Models of Theories with Constraints in Interpretation

We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as well as to the analysis of models of certain theories with constraints in interpretation (TCIs). The foundations for a theory of TCIs and their models are laid in parallel to the development of our framework, and are of independent interest.

math.LO↗