## A Kolmogorov shift with no roots |

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### Contents

HISTORICAL BACKGROUNDSOME FACTSSOME | 3 |

SECTION | 5 |

k T P IS ERGODIC | 13 |

5 other sections not shown

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### Common terms and phrases

account of lemma argument assertion follows bad terms base of G Bernoulli Shifts blocks called code f column of G Conditional entropy conditional expectation congruent copy construction contributes at least copies of G copy G corresponding to g defined definition of replicas disjoint Doctor of Philosophy double overlap e-levels entropy ergodic Ergodic Theory G columns G in G gadgets G Gffl height of G integer interval invertible measure preserving K-automorphisms K-shifts KOLMOGOROV SHIFT law of large least eN bad lemma 9 letter m-bad terms m+n)-block m+n+1 mAmBl measure of G measure preserving mapping multiple n-block n-l)-blocks name of x Pairwise independence partition piece in G pth root replicas of G rigidity lemmas satisfy Section semi-bad terms sequence sigma-algebra Suppose tail field tier of G top of G total number Tp,P name union wlog zero-blocks