clone lattice
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2013 ◽  
Vol 23 (05) ◽  
pp. 1115-1125
Author(s):  
MARTIN GOLDSTERN ◽  
MICHAEL PINSKER ◽  
SAHARON SHELAH

Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is not Borel. Moreover, we provide an example of a coatom in the clone lattice whose obvious definition via an ideal of subsets of natural numbers would suggest that it is complete coanalytic, but which turns out to be a rather simple Borel set.


2009 ◽  
Vol 62 (4) ◽  
pp. 367-374
Author(s):  
Martin Goldstern ◽  
Saharon Shelah
Keyword(s):  

2009 ◽  
Vol 19 (03) ◽  
pp. 397-421 ◽  
Author(s):  
MATHIAS BEIGLBÖCK ◽  
MARTIN GOLDSTERN ◽  
LUTZ HEINDORF ◽  
MICHAEL PINSKER
Keyword(s):  

On an infinite base set X, every ideal of subsets of X can be associated with the clone of those operations on X which map small sets to small sets. We continue earlier investigations on the position of such clones in the clone lattice.


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