Logic

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Quote

Logic = not illogical

Logic is the branch of mathematics dealing with reasoning.

It is used to create a syntax that is used to describe mathematical statements and talks about its semantics

Error

cannot think of an introduction, if you have ideas, send send.

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Course Notes

• First Order Logic
  • Syntax of First Order Logic
  • Semantics of First Order Logic
  • Groups In First Order Logic
  • Isomorphism Between First Order Interpretations
• Ehrenfeucht-Fraïssé Game
  • Ehrenfeucht-Fraïssé Theorem
  • Rank-k Types (FO)
  • Partial Isomorphism
  • Even is not FO-definable for Linear Orders
• Quanitifier Elimination for Natural Numbers With Successor
  • Natural Numbers with Successor
  • Natural Numbers with Successor and Ordering
  • Decidability of Presburger Arithmetic
  • N_L admits Quantifier Elimination
  • Natural Numbers with Successor Function is Complete
  • Los-Vaught Test

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Notes

• Ordering between Axiomatic Theories
• Lindenbaum-Tarski Algebra
  • Boolean Algebra
  • Heyting Algebra
  • Frames(Algebra)

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MOCs

• Logic, Automata and Games
• Revisiting Complexity of First-Order and Monadic-Second-Order Logic
• Type Theory
• Set Theory

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References