By Kalantari I., Welch L.
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Extra info for A blend of methods of recursion theory and topology: A П 0^1 tree of shadow points
The refleation in the line a or the point A, respectively. Let F(a) denote the set of fixed points of the motion induced by a: Pta) : tx E P: Xa = X}. d is called the fourth reflection line to a,b,a, if aba = = d. ar to b (We denote this line by (A,b)); (2) Three lines which have a common perpendiaular have a fourth reflection line; (3) If A,c are incident, then Aa is a line (This implies the special case of (Sp)); (4) There are two orthogonal lines. A pair (C,S) which has all these properties shall be called a perpendicularity group.
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Automorphism in K). lJ k c c -1 k' k' k -1. e. 1 ) If P F 2 (whence oK = pr by lemma 3), then k21 F k21 by lemma 4. ) = (k . )a. Since a E Z(H) (lemma 5) we have 2 Y2 lJ 2 lJ 2 ((k .. ) )Y = ((k .. ) = (k .. )a(k . )a = (k .. ) • Thus Y should fix the nonlJ lJ lJ 2 lJ lJ lJ -1 identical collineation (k ij ) of K. 2) If x~ 1 4 E d .. xe. are the equations that define the collineation = j=l lJ J v of N, we C. Bart%ne 46 may set d .. = 0 for i < j (see remark 2). N lJ U = U and L(N) i > j. 2), we notice that d ..