Logic of Ruler and Compass Constructions

@inproceedings{Beeson2012LogicOR,
  title={Logic of Ruler and Compass Constructions},
  author={Michael Beeson},
  booktitle={CiE},
  year={2012}
}
We describe a theory ECG of “Euclidean constructive geometry”. Things that ECG proves to exist can be constructed with ruler and compass. ECG permits us to make constructive distinctions between different forms of the parallel postulate. We show that Euclid’s version, which says that under certain circumstances two lines meet (i.e., a point of intersection exists) is not constructively equivalent to the more modern version, which makes no existence assertion but only says there cannot be two… CONTINUE READING
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