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first_order_interpretation (581B)

      1 # First order interpretation
      2 
      3 A *d-dimensional FO interpretation* defines:
      4 
      5 - an [FO] formula of arity d for domain elements, among d-tuples
      6 - an [FO] formula of arity 2d, for equality
      7   - we take the [quotient] under it
      8 - [FO] formulas of arity dk to define [relations] of arity k
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     10 This allows [formulas] on the image of the FO interpretation to be "translated back" to the source of the FO interpretation
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     12 We can get rid of equality, cf [morvan2025homomorphism], Prop VII.3.2
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     14 Up: [logic_interpretation], [FO]
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     16 Aliases: FO interpretation, FO reduction
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     18 See also: [FO_projection]