Logic: Lecture 20, 01 November 2012
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Tarski:  Given that (N,0,+,.) is undecidable, can we extend
         (N,0,S) in another dimension?

First order vs second order logic

Monadic second order logic: 

  Quantify over unary relations
  Equivalent to adding set quantifiers:

Examples:

  Principle of Mathematical Induction 
  x < y
  Evenness

Restrict to finite models

  Additional constants min, max

Add labels to positions

  Interpret over words over a finite alphabet

Examples of definable languages

  Words starting with a
  Words with at least 2 b's

Digression finite automata

  DFAs
  Complete and incomplete DFAs
  Unique run, complementation
  Checking emptiness