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math.LO2026
The Gamified KatÄtov order is not linear (in fact, very much not so)
Takayuki Kihara, Ming Ng
Recently, the authors introduced the Gamified KatÄtov order on filters over . This was shown to be strictly coarser than the classical KatÄtov order, and in fact collapses al…
math.LO2026
What can Topology tell us about Logical Complexity?
Takayuki Kihara, Ming Ng
In the 1980s, category theorists introduced the Lawvere-Tierney order in the Effective Topos, known to effectively embed the Turing degrees. Understanding it…
math.LO2026
The Game-Theoretic KatÄtov Order and Idealised Effective Subtoposes
Takayuki Kihara, Ming Ng
This paper addresses the longstanding problem of determining the structure of the -order in the Effective Topos, known to effectively embed the Turing degrees.…