Recursion Theory/Descriptive Set Theory Seminar - Fall 2026

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Time: Fridays 11:00-12:30
Location: 939 Evans Hall
Topic: Priority arguments and true stages in recursion theory and descriptive set theory. We will discuss some the method of true stages in computability theory and some applictions, before discussing some more recent uses of priority arguments and true stages in descriptive set theory

References:

• Montalbán: computable structure theory: Part I: Within the arithmetic and Part II: Beyond the arithmetic.
• Solecki (1998) Decomposing Borel sets and functions and the structure of Baire class 1 functions, J. Amer. Math. Soc. 11 (1998), 521-550.
• Pawlikowski, Sabok (2012) Decomposing Borel functions and structure at finite levels of the Baire hierarchy
• Solecki (2021) Transfinite sequences of topologies, descriptive complexity, and approximating equivalence relations, Isr. J. Math. 242, 933-953
• Greenberg, Lecompte, Turetsky, Zelen (2026) Topology, forcing, and graph colourings
• Papers in progress by Day, Montalbán, Weilacher, myself, and others

Other related papers:

• Zapletal (2004) Descriptive Set Theory and Definable Forcing, Memoirs of the AMS, see section 2.3.13 on Steprans forcing
• Lutz (2023) The Solecki Dichotomy and the Posner-Robinson Theorem are Almost Equivalent
• Day, Greenberg, Harrison-Trainor, Turetsky (2024) Iterated Priority Arguments in Descriptive Set Theory, Bulletin of Symbolic Logic, Vol. 30 (2), June 2024, pp. 199-226

Tentative schedule:

• Aug 28: Organizational meeting
• Sep 4: (Yvette) Introduction to True Stages (Chapter 7 of Montalbán part I)
• Sep 11: (Antonio) More on True Stages
• Sep 18: (Ted) Ted Talk: TBA
• Sep 25: (Daniel) Scott analysis (Chapter 2.1 of Montalbán part II)
• Oct 2: (Daniel) Back and Forth Relations (Chapter 2.6 of Montalbán part II)
• Oct 9: (Jad) The game metatheorem and pair of structures theorem (Chapter 8 of Montalbán part II)
• Oct 16: (Antonio) Iterated true stages and the tree of structures theorem (Chapter 9 of Montalbán part II)
• Oct 23: (Suyash) The Solecki dichotomy
• Oct 30: (Felix) Filtrations and examples from Steel forcing, Scott analysis, and Louveau's topologies
• Nov 6: (Francesca) The level-by-level G_0 dichotomy of Greenberg, Lecompte, Turetsky, and Zeleny
• Nov 13: (Alex) A topological metatheorem
• Nov 20: (Felix) Applications of the topological metatheorem
• Dec 4: (Andrew) The decomposability conjecture