The reason that structures have footings is the phenominon of
frost heave. Certain types of soil contain and transmit water, that freezing, create
ice lenses, that lift the structure out of the soil.
There are two ways to combat frost heave. One is brute force. You dig down below the frost line, and you pour footings 12 inches thick, protruding six inches beyond the outside of the structure.
The other is to avoid the problem by creating an artificial soil that is not subject to water wicking. You do this by laying down six inches of well drained crushed rock below your slab. This porous layer doesn't get saturated with water, so even if it freezes, it doesn't form the dreaded ice lenses. In order for this to work, the area for the oven must not be in the lowest part of the garden where puddles form in heavy rains.
Here's a quote from the last link, the Canadian Building Digest:
Quote:
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Where a detached building is located on a concrete slab on grade, protection will be provided by placing the slab on a mat of coarse granular material, which will act as a buffer against any movement of the soil under the mat. A mat 12 to 18 in. in thickness is usually adequate.
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Just my opinion, but if it's good enough for Canada, it's good enough for Michigan.
All this is moot, if the oven is part of the house or other structure, or if you plan a tall masonry chimney. Then you must have proper footings, as per masonry fireplace building code.