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start [2025/02/10 16:32] – [How to contribute?] lpateystart [2025/02/12 10:21] (current) – [Topics] lpatey
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-====== Computability Theory Wiki ======+====== Computability theory wiki ======
  
-Welcome to the **Computability Theory Wiki**, a comprehensive resource dedicated to the study of computability and recursion theory. This wiki aims to provide clear and rigorous definitions of core terminology, as well as structured mini-courses to facilitate learning at different levels.+Welcome to the **Computability theory wiki**, a comprehensive resource dedicated to the study of computability and recursion theory. This wiki aims to provide clear and rigorous definitions of core terminology, as well as structured mini-courses to facilitate learning at different levels. See the [[http://portal.computability.org|computability portal]] for a list of [[http://portal.computability.org/directory|members]], [[http://portal.computability.org/books|books]], [[http://portal.computability.org/publications|articles]] and [[http://portal.computability.org/videos|videos]] on the subject.
  
-===== What You Will Find Here =====+===== What you will find here =====
   * **Definitions** – Precise explanations of key concepts in computability theory, such as Turing machines, recursive functions, and degrees of unsolvability.   * **Definitions** – Precise explanations of key concepts in computability theory, such as Turing machines, recursive functions, and degrees of unsolvability.
   * **Mini-courses** – Structured lessons ranging from introductory topics to advanced subjects in computability and logic.   * **Mini-courses** – Structured lessons ranging from introductory topics to advanced subjects in computability and logic.
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   * [[introduction:computability|Computability theory in a nutshell]]   * [[introduction:computability|Computability theory in a nutshell]]
  
 +
 +===== Main theorems =====
 +
 +  * [[theorem:rice|Rice's theorem]]
 +  * [[theorem:smn|SMN theorem]]
 +  * [[theorem:undecidability_halting_set|Undecidability of the halting set]]
 +
 +
 +===== Main concepts =====
 +
 +  * [[turing_degree|Turing degree]]
 +
 +
 +===== Topics =====
 +
 +
 +  * [[topic:sets_sequences_reals|Sets, sequences and real numbers]]
 +  * [[topic:incompleteness_paradox|Incompleteness theorems as paradoxes]]
 +  * [[topic:set_reducibilities|Reducibilities on sets]]
 +  * [[topic:problem_reducibilities|Reducibilities on problems]]
  
 ===== Learning material ===== ===== Learning material =====
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  • Last modified: 2025/02/10 16:32
  • by lpatey